9967108800 has 378 divisors, whose sum is σ = 36219911812. Its totient is φ = 2397824000.

The previous prime is 9967108769. The next prime is 9967108807. The reversal of 9967108800 is 88017699.

It is a happy number.

It is a Harshad number since it is a multiple of its sum of digits (48).

It is a self number, because there is not a number n which added to its sum of digits gives 9967108800.

It is not an unprimeable number, because it can be changed into a prime (9967108807) by changing a digit.

It is a polite number, since it can be written in 53 ways as a sum of consecutive naturals, for example, 76084735 + ... + 76084865.

Almost surely, 2^9967108800 is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 9967108800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (18109955906).

9967108800 is an abundant number, since it is smaller than the sum of its proper divisors (26252803012).

It is a pseudoperfect number, because it is the sum of a subset of its proper divisors.

9967108800 is a wasteful number, since it uses less digits than its factorization.

9967108800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 309 (or 152 counting only the distinct ones).

The product of its (nonzero) digits is 217728, while the sum is 48.

The square root of 9967108800 is about 99835.4085482701. The cubic root of 9967108800 is about 2152.0700308420.

Multiplying 9967108800 by its sum of digits (48), we get a square (478421222400 = 691680²).

9967108800 divided by its sum of digits (48) gives a square (207648100 = 14410²).

The spelling of 9967108800 in words is "nine billion, nine hundred sixty-seven million, one hundred eight thousand, eight hundred".